Developing predictive dose-volume relationships for a radiotherapy treatment

ABSTRACT

Embodiments develop a predictive dose-volume relationships for a radiation therapy treatment is provided. A system includes a memory area for storing data corresponding to a plurality of patients, wherein the data comprises a three-dimensional representation of the planning target volume and one or more organs-at-risk. The data further comprises an amount of radiation delivered to the planning target volume and the one or more organs-at-risk. The system further includes one or more processors programmed to access, from the memory area, the data and to develop a model that predicts dose-volume relationships using the three-dimensional representations of the planning target volume and the one or more organs-at-risk. The model is being derived from correlations between dose-volume relationships and calculated minimum distance vectors between discrete volume elements of the one or more organs-at-risk and a boundary surface of the planning target volume.

CROSS REFERENCE TO RELATED APPLICATION

This application claims priority to U.S. Provisional Patent ApplicationNo. 61/493,415, filed Jun. 3, 2011, and U.S. patent application Ser. No.13/486,809, filed Jun. 1, 2012, the entire disclosures of which arehereby incorporated by reference in their entireties.

BACKGROUND

Conventional radiation therapy techniques include the use of IntensityModulated Radiation Therapy (“IMRT”), Arc Therapy, Three-DimensionalConformal Radiation Therapy (“3-D CRT”), Particle Therapy, orBrachytherapy. The use of IMRT, for example, allows a radiationoncologist to treat a patient from multiple angles while varying theshape and dose of a radiation beam and thereby providing greatlyenhanced ability to deliver radiation to a region of interest whileavoiding excess irradiation of nearby healthy tissue.

Various treatment planning optimization techniques exist for developingradiation fluence patterns for external beam radiation therapy treatmentplans. Treatment planning starts typically with images of an area ofinterest (e.g., slices from a CT scan), a desired dose of radiationwhich is to be delivered to a region of interest, such as a tumor, and“organs-at-risk” (OAR), which represent healthy tissues that areadjacent to or near the area of interest. A portion of a patient'sanatomy that is intended to receive a therapeutic prescribed dose isreferred to as a “planning target volume” (PTV). Both the PTV and anyOAR may have complex three-dimensional shapes adding to the difficultyof preparing a treatment plan.

A variety of algorithms have been developed to solve an “inverseproblem” of devising and optimizing a three-dimensional treatment planfor irradiating a planning target volume from a variety of angles todeliver a desired radiation dose to a region of interest whileminimizing irradiation of nearby tissue (e.g., an OAR). Conventionaltreatment planning software packages are designed to import 3-D imagesfrom a diagnostic imaging source, for example, x-ray computed tomography(CT) scans. CT is able to provide an accurate three-dimensional model ofa volume of interest (e.g., tumor bearing portion of the body) generatedfrom a collection of CT slices and, thereby, the volume requiringtreatment can be visualized in three dimensions.

During radiotherapy planning, volumetric structures are delineated to betargeted or avoided with respect to the administered radiation dose.That is, the radiation source is positioned in a sequence calculated todeliver the radiation dose that as closely as possible conforms to thetumor requiring treatment, while avoiding exposure of nearby healthytissue (e.g., OAR). Once the region of interest (e.g., tumor) has beendefined, and the critical normally-functioning tissue volumes have beenspecified, the responsible radiation oncologist specifies a desiredradiation dose to the PTV and the allowable dose to OARS. Guided by atreatment planner or medical physicist, the software then produces atreatment plan that attempts to meet clinical dosimetric objectivesexpressed in terms of “dose-volume relationships.” These dose-volumerelationships range from simple single-valued metrics mean dose) to thethree-dimensional dose matrix itself. One commonly used embodiment of adose-volume relationship is the dose-volume histogram (DVH) thatsummarizes the frequency distribution of radiation doses in a particularvolumetric structure (PTV or OAR).

However, the above methods allow a planner to change objective criteriaand guide inverse planning algorithms to a case-by-case solution, whichthen undergoes clinical review by a radiation oncologist before apatient is treated. Thus, the evaluation criteria are very subjectiveand depend on a planner's level of experience and an amount of time theplanner has in developing the plan. In addition, planners and reviewersoften accept plans when further sparing of an OAR is possible.

SUMMARY

In one aspect, a system for developing a predictive dose-volumerelationship for an intensity modulated radiation therapy treatment isprovided. The system includes a memory area for storing datacorresponding to a plurality of patients, wherein the data comprises athree-dimensional representation of the planning target volume and oneor more organs-at-risk. The data further comprises an amount ofradiation delivered to the planning target volume and the one or moreorgans-at-risk. The system further includes one or more processorsprogrammed to access, from the memory area, the data corresponding tothe plurality of patients, the data comprising a three-dimensionalrepresentation of the planning target volume and one or moreorgans-at-risk, and the data comprising an amount of radiation deliveredto the planning target volume and the one or more organs-at-risk. Theprocessor is also programmed to develop a model that predictsdose-volume relationships using the three-dimensional representations ofthe planning target volume and the one or more organs-at-risk. The modelis being derived from correlations between dose-volume relationships andcalculated minimum distance vectors between discrete volume elements ofthe one or more organs-at-risk and a boundary surface of the planningtarget volume. Alternatively, there could may other suitable methods toderive the model.

In another aspect, a method is provided. The method includes receivingdata corresponding to a radiation of a planning target volume in aplurality of patients, wherein the data comprises a three-dimensionalrepresentation of the planning target volume and one or moreorgans-at-risk. The data further comprises an amount of radiationdelivered to the planning target volume and the one or moreorgans-at-risk, and based on the received data. The method also includesdetermining a predictive dose-volume relationship for irradiating theplanning target volume while sparing organs-at-risk.

In yet another aspect, one or more storage media embodyingcomputer-executable components are provided. The components include aninterface component that when executed by at least one processor causesthe at least one processor to receive data corresponding to a radiationof a planning target volume in a plurality of patients. The datacomprises a three-dimensional representation of the planning targetvolume and one or more organs-at-risk. The data further comprises anamount of radiation delivered to the planning target volume and the oneor more organs-at-risk. The components also include a correlationcomponent that when executed by the at least one processor causes the atleast one processor to determine predictive dose-volume relationshipsfor sparing organs-at-risk while irradiating the planning target volumebased on the received data.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an exemplary block diagram of a system for developing apredictive dose-volume relationship for an IMRT treatment.

FIG. 2 is an exemplary flow chart illustrating a process for developingpredictive dose-volume relationships for a radiation therapy treatmentand applying that model to predict the dose-volume relationships in anew patient.

FIGS. 3A-3B depict the boundary distance vector and scalar fields.

FIG. 4 is a schematic diagram of geometric constructs.

FIGS. 5A and 5B are graphs depicting associated differential andcumulative dose-volume histograms, respectively. The sub-DVHs Xijkrepresent the differential DVHs of the sub-volume elements Aijk depictedin FIG. 4.

FIGS. 6A-6D are graphs depicting fits to rectum sub-volume DVHs with ageneralized mathematical function.

FIG. 7 is a graph depicting a representation of in-field andout-of-field OAR for prostate and rectum, a geometric distinctionimportant in co-planar radiotherapy deliveries.

FIG. 8A-8F are depicting in-field rectum parameters and fitting.

FIGS. 9A-9C are graphs depicting goodness-of-fit and outlieridentification analyses using analysis of the cumulative DVHs.

FIGS. 10A and 10B are block diagrams depicting a two-stage validation ofpredictive DVH modeling.

FIGS. 11A-11L are graphs depicting distribution of parameters andgeneralized polynomial fits for rectum and bladder in intact prostateIMRT with a 20-patient training cohort.

FIGS. 12A-12F are graphs demonstrating the concordance of two predictiveDVH models to the clinically-approved rectum and bladder DVHs from thetraining set.

FIGS. 13A and 13B are graphs depicting correlation between predictedgains and gains realized through re-planning, validating the rectum andbladder models' ability to correctly distinguish optimal and sub-optimaltreatment plans.

FIGS. 14A-14F are graphs depicting predicted rectum and bladder DVHscorrectly identifying plans that could be improved under replanning.

FIGS. 15A-15F are graphs demonstrating the concordance of two predictiveDVH models to the clinically-approved rectum and bladder DVHs from thevalidation set, i.e. “new” plans unseen by the model.

FIGS. 16A-16F are graphs depicting parotid in-field and out-of-fieldparameter trajectories.

FIGS. 17A-17F are graphs demonstrating the concordance of two predictiveDVH models to clinically-approved parotid DVHs from the training set.

FIGS. 18A-18C are graphs depicting predicted parotid DVHs correctlyidentifying plans that could be improved under re-planning.

FIG. 19 demonstrates the correlation between predicted gains and gainsrealized through re-planning, validating the parotid model's ability tocorrectly distinguish optimal and sub-optimal treatment plans.

Corresponding reference characters indicate corresponding partsthroughout the drawings bound.

DETAILED DESCRIPTION

One feature of an effective radiation treatment system is homogeneity ofdose delivered to the intended target of the therapeutic radiation.Homogeneity is the uniformity of a radiation dose over a volume of aplanning target volume (e.g., pathological anatomy such as a tumor,lesion, vascular malformation, and the like).

Another feature of an effective radiation treatment is the sparing, tothe highest degree possible, of the normally-functioning tissuesurrounding the PTV from the ancillary radiation needed to deliver thetherapeutic dose to the PTV. This can be expressed in many ways thatdescribe the distribution of radiation across an organ-at-risk, relatingthe dose to the volumetric representation of the OAR. One suchexpression of a dose-volume relationship is the dose-volume histogram,i.e. a summary of the distribution of radiation deposition in aparticular structure (PTV or OAR).

A variety of algorithms have been developed to solve an “inverseproblem” of devising and optimizing a three-dimensional treatment planto deliver a desired radiation dose to an area of interest whileminimizing irradiation of nearby tissue. Currently, however, plannersmanually tweak planning elements (e.g., inverse planning optimizationparameters) to optimize a treatment plan until it is deemed to beclinically acceptable. As such, Intensity Modulated Radiation Therapy(“IMRT”) planning can be both subjective and time-consuming process oftrial-and-error. Even if the human elements of this problem areeliminated through planning automation, quality control methods would berequired to verify that the product of such automation has been properlyimplemented with respect to past experience.

The present disclosure provides a system and method for developing apredictive dose-volume relationship (in this embodiment, a dose-volumehistogram) for a radiation therapy treatment based on geometricmeasurements, such as boundary distance vectors. The system and methodcorrelates the three-dimensional representation of the PTV and the oneor more OAR, represented in this embodiment by a calculated set ofminimum magnitude distance vectors between organ voxels and the boundarysurface of the planning target volume (hereby referred to as “boundarydistance vectors”). The predictive dose-volume relationship is based ondata from a prior training set of patients, whereby the system andmethod establishes a functional relationship between boundary distancevectors and a probability distribution of radiation dose for an organvoxel at that position.

Referring now to FIG. 1, an exemplary block diagram of a system 100 isprovided. System 100 is but one example of a suitable system and is notintended to suggest any limitation as to the scope of use orfunctionality of the present disclosure. Further, system 100 should notbe interpreted as having any dependency or requirement relating to anyone or combination of components illustrated herein.

System 100 includes a computing device 102, a network 104, and a server106. While some embodiments of the disclosure are illustrated anddescribed herein with reference to the server 106 being a servercomputing device, aspects of the disclosure are operable with any devicethat performs the functionality illustrated and described herein, or itsequivalent, such as in peer-to-peer systems. For example, embodiments ofthe disclosure are operable with netbooks, desktop computing devices,laptop computers, and other computing devices. In such embodiments, datamay be stored by a cloud service and accessible by any computing deviceimplementing functionality of the disclosure.

Referring again to FIG. 1, an exemplary block diagram illustrates thecomputing device 102 having a memory area 108 for storing components fordeveloping a predictive dose-volume relationship for a radiotherapytreatment. Computing device 108 further includes a display 110 and atleast one processor 112. Display 110 may be, for example, a capacitivetouch screen display that is integrated into computing device 102 orexternal to computing device 102. User input functionality is providedin display 110 which acts as a user input selection device as well as ameans to provide a user with a predictive dose-volume relationship. Inembodiments, display 110 is configured to be responsive to a userpressing contact on display 110 to selectively perform functionality.Thus, a user can operate the desired troubleshooting functions availablewith computing device 102 by contacting a surface of display 110 as wellas other functions provided herein.

Memory area 108 stores radiation data 114 corresponding to anirradiation of a PTV (not shown) in a plurality of patients. Radiationdata 114 includes a three-dimensional representation of a PTV and one ormore OAR (not shown) for each patient's treatment. Radiation data 114further includes an amount of radiation delivered to the PTV and any OARas well as one or more computer-executable components. Exemplarycomponents include, but are not limited to, an interface component 116,a correlation component 118, and a display component 120. Whileradiation data 114 and components 116-120 are shown to be stored inmemory area 108, radiation data 114 and components 116-120 may be storedand executed from a memory area remote from computing device 102. Forexample, radiation data 114 may be stored in a cloud service, adatabase, or other memory area accessible by computing device 102. Suchembodiments reduce the computational and storage burden on computingdevice 102.

Processor 112 executes computer-executable instructions for implementingaspects of the disclosure. In some embodiments, processor 112 istransformed into a special purpose microprocessor by executing;computer-executable instructions or by otherwise being programmed. Forexample, processor 112 may execute interface component 116 andcorrelation component 118.

Interface component 116, when executed by the processor 112, causes theprocessor 112 to access, from memory area 108, radiation data 114corresponding to a radiation of a planning target volume in a pluralityof patients. In one embodiment, radiation data 114 includes athree-dimensional representation of the PTV and one or more OAR for atreatment corresponding to each of the plurality of patients. Radiationdata 114 further includes an amount of radiation delivered to the PTVand the one or more OAR for a treatment corresponding to each of theplurality of patients. Correlation component 118, when executed by theprocessor 112, causes the processor 112 to determine predictivedose-volume relationships for the PTV and the one or more OAR.

In general, processor 112 may be programmed with instructions such asdescribed herein with reference to the components illustrated in FIG. 1,and the operations illustrated and next described in FIG. 3.

Referring next to FIG. 2, an exemplary flow chart illustrates a processfor developing a predictive dose-volume relationship for a radiotherapytreatment. At 202, radiation data corresponding to a radiation of a PTVin a plurality of patients is received. The radiation data includes athree-dimensional representation of the PTV and one or more OAR, as wellas an amount of radiation delivered to the PTV and the one or more OAR.Based on a model that is developed through an analysis of priortreatment plans, and in particular, using geometric measurements (e.g.,boundary distance vectors) from the radiation data as the determiningdosimetric feature, a dose-volume relationship (e.g., a DVH) of aradiotherapy plan can be predicted.

At 204, a predictive dose-volume relationship is determined based on thereceived data. In one embodiment, the predictive dose-volumerelationship is determined by first calculating a dose-volumerelationship corresponding to the irradiation of the PTV for eachpatient, and thereafter determining a correlation between the calculatedDVHs and the set of boundary distances from the one or more OAR to thePTV. At 206, the predictive dose-volume relationship is optimized. Inone embodiment, optimizing the predictive dose-volume relationshipincludes comparing the predictive dose-volume relationship to each ofthe calculated dose-volume relationships and determining which of thecalculated dose-volume relationships are optimal based on the comparing.In one embodiment, once the optimal dose-volume relationships aredetermined, a model embodying the correlation between the optimaldose-volume relationships and the boundary distance vectors from the oneor more OAR to the PTV is determined. To employ the resultant model,data corresponding to the three-dimensional representation of the PTVand the one or more OAR of a new patient is received. The data is inputto the model and the predicted dose-volume relationships for the PTV andthe one or more OAR are calculated and presented.

Exemplary Operating Environment

A computer or computing device such as computing device 102 and server106 described herein have one or more processors or processing units,system memory, and some form of computer readable media. By way ofexample and not limitation, computer readable media comprise computerstorage media and communication media. Computer storage media includevolatile and nonvolatile, removable and non-removable media implementedin any method or technology for storage of information such as computerreadable instructions, data structures, program modules or other data.Communication media typically embody computer readable instructions,data structures, program modules, or other data in a modulated datasignal such as a carrier wave or other transport mechanism and includeany information delivery media. Combinations of any of the above arealso included within the scope of computer readable media.

The computer may operate in a networked environment using logicalconnections to one or more remote computers, such as a remote computer.Although described in connection with an exemplary computing systemenvironment, embodiments of the invention are operational with numerousother general purpose or special purpose computing system environmentsor configurations. The computing system environment is not intended tosuggest any limitation as to the scope of use or functionality of anyaspect of the invention. Moreover, the computing system environmentshould not be interpreted as having any dependency or requirementrelating to any one or combination of components illustrated in theexemplary operating environment. Examples of well known computingsystems, environments, and/or configurations that may be suitable foruse with aspects of the invention include, but are not limited to,personal computers, server computers, hand-held or laptop devices,multiprocessor systems, microprocessor-based systems, set top boxes,programmable consumer electronics, mobile telephones, network PCs,minicomputers, mainframe computers, distributed computing environmentsthat include any of the above systems or devices, and the like.

Embodiments of the invention may be described in the general context ofcomputer-executable instructions, such as program modules, executed byone or more computers or other devices. The computer-executableinstructions may be organized into one or more computer-executablecomponents or modules. Generally, program modules include, but are notlimited to, routines, programs, objects, components, and data structuresthat perform particular tasks or implement particular abstract datatypes. Aspects of the invention may be implemented with any number andorganization of such components or modules. For example, aspects of theinvention are not limited to the specific computer-executableinstructions or the specific components or modules illustrated in thefigures and described herein. Other embodiments of the invention mayinclude different computer-executable instructions or components havingmore or less functionality than illustrated and described herein.Aspects of the invention may also be practiced in distributed computingenvironments where tasks are performed by remote processing devices thatare linked through a communications network. In a distributed computingenvironment, program modules may be located in both local and remotecomputer storage media including memory storage devices.

Aspects of the invention transform a general-purpose computer into aspecial-purpose computing device when configured to execute theinstructions described herein.

The embodiments of the system and method for developing a predictivedose-volume relationship for an intensity modulated radiation therapytreatment, as described herein, were used in the following exemplaryexperiment.

EXPERIMENT

In this experiment, which represents one possible embodiment of thisdisclosure, a framework to predict achievable OAR DVHs was derived basedon a correlation of expected dose to the distance from a voxel to thePTV surface (r). OAR voxels sharing a range of r were computed assub-volumes. A three-parameter, skew-normal probability distribution wasused to fit sub-volume dose distributions, and DVH prediction modelswere developed by fitting the evolution of the skew-normal parameters asa function of r with generalized polynomials. A cohort of 20 prostateand 24 head-and-neck IMRT plans with identical clinical objectives wereused to train organ-specific AVERAGE models for rectum, bladder, andparotid glands. A sum of residuals analysis quantifying the integrateddifference between DVHs was utilized to score the concordance of one DVHto another. The AVERAGE model's predictive ability was evaluated byapplication of the model to an independent validation cohort of 20prostate IMRT plans (i.e. “new” patients as yet unseen by the model).Statistical comparison of the residual sums between the training andvalidation cohort quantified the accuracy of the AVERAGE model.Restricted sums of residuals that ignore regions where the clinical DVHis better use the predicted DVH to identify potentially sub-optimalplans, wherein sub-optimality is defined to be a case where the clinicalOAR DVH was in demonstrable excess of a model's prediction. A REFINEDmodel for each organ was obtained by excluding cases from the trainingcohort with restricted residual sums. The REFINED model was thenre-applied to the entire training cohort with the restricted such ofresiduals for this cohort representing the best estimate of thepotential case-by-case improvement. All training cases were re-plannedand re-evaluated by the attending physician that approved the originalclinical plan to ensure clinical acceptability of the new solutions. Theresidual sum between the original and re-planned DVHs represented therealized gains under re-planning, quantifying the accuracy of theREFINED model's outlier identification.

As described in more detail below, the results of this study demonstratethe ability to predict achievable OAR DVHs based on individual patientanatomy. The models were further capable of identifying sub-optimalplans that were subsequently brought within expected values via furtheroptimization. This technique requires no manual intervention except forthe appropriate selection of previous treatment plans with identicalclinical quality evaluation criteria.

To understand the process of making prospective dosimetric predictions,the clinical goals of the IMRT planning process should be considered.For example, as shown below, Table 1 enumerates exemplary planning goalsfor prostate and head-and-neck. All treatment plans considered in thisstudy attempted to meet these common goals, though the degree to whichany individual plan optimally satisfied the multi-objective list wasvariable and previously unquantified.

This first goal of this experiment is to derive the mathematicallearning framework necessary to, given a sufficient training set ofclinical data, predict the expected OAR dose-volume histogram (DVH) forfuture cases based only on organ geometry. An automated framework fordetection and rejection of sub-optimal plans from the training cohort isthe second goal. Finally, this experiment seeks to provide a methodologyfor validating the two primary functions of predictive DVHs: (1)accurate dosimetric forecasting and (b) sensitive and specific detectionof sub-optimal plans.

TABLE 1 Exemplary IMRT planning goals for prostate and head-and-necktreatments. Objectives Site PTV/OAR In-tact Prostate Prostate PTV 98% ofPTV receives 100% of Rx; Maximum dose < 107% of Rx Rectum V65 < 17%; V40< 35%; Maxiumum dose as low as possible Bladder V65 < 25%; V40 < 50%;Maxiumum dose as low as possible Femoral Heads V50 < 10% of the totalvolume Unspecified Tissue Less than PTV dose; <5% exceeds PTV doseBilateral Neck Treatment Ipsilateral Neck Treatment H&N PTV 95% of PTV >95% of Rx; Max dose < 110% of Rx 95% of PTV > 95% of Rx; Max dose < 110%of Rx Spinal Cord Max dose 40 Gy Max dose 40 Gy Spinal Cord + Margin Maxdose 52 Gy; <1% (or 1 cc) exceeds 50 Gy Max dose 52 Gy; <1% (or 1 cc)exceeds 50 Gy Optic Nerves, Max dose 54 Gy Max dose 54 Gy Optic ChiasmBrainstem Max dose 54 Gy; <1% exceeds 60 Gy Max dose 54 Gy; <1% exceeds60 Gy Brain Max dose 60 Gy; <1% exceeds 65 Gy Max dose 60 Gy; <1%exceeds 65 Gy Retina Max dose 50 Gy; <5% exceeds 45 Gy Max dose 50 Gy;<5% exceeds 45 Gy Larynx As low as possible; mean Dose < 45 Gy As low aspossible; mean Dose < 25 Gy Upper Esophagus As low as possible; meanDose < 45 Gy As low as possible; mean Dose < 25 Gy Parotid Mean dose ≤26 Gy (at least one parotid) Mean dose < 10 Gy (contralateral parotid)Pharyngeal Constrictors As low as possible; V60 < 60 Gy As low aspossible; V60 < 45 Gy Submandibular Mean dose < 39 Gy Mean dose < 24 Gy(contralateral) Oral Cavity As low as possible; mean Dose under 35 Gy Aslow as possible; mean Dose < 20 Gy Mandible Max 70 Gy; <5% exceeds PTVRx Max 70 Gy; <5% exceeds PTV Rx Unspecified Tissue Less than PTV Rx;<5% exceeds PTV Rx Less than PTV Rx; <5% exceeds PTV Rx

The starting assumption for this work involves the identification of acohort of N site-similar IMRT plans that were developed using identicalclinical goals and quality assessment criteria. The planning datasetsare comprised of structure sets SSij (i=l . . . N cases, j=l . . . Mstructures with j=1 representing the PTV and j=2 . . . M representingM−1 OARs) and dose matrices D_(i)=D_(i)({right arrow over (x)}), where{right arrow over (x)} is the 3-D position vector with arbitrary origin.Operations on SS_(ij) and D_(i) result in differential DVH

$v_{ij}^{r} = \left( \frac{{dV}_{j}}{dD} \right)_{i}$for the j^(th) OAR in the dataset, and summing

${V\left( {SS}_{ij} \right)} = {\sum\limits_{D = 0}^{\infty}\;{{\left( \frac{{dV}_{j}}{dD} \right)_{i} \cdot \Delta}\; D}}$over a set of discreet dose bins (ΔD) yields the OAR volume. Theproblems may be simplified by normalizing the dose matrices to the PTVprescription dose, i.e.

$\left. D_{i}\rightarrow\frac{D_{i}}{D_{Rx}} \right.,$and employing normalized differential DVHs, i.e.

$\left. V_{ij}^{\prime}\rightarrow{\frac{V_{ij}^{\prime}}{V\left( {SS}_{ij} \right)}.} \right.$Finally, the familiar normalized cumulative DVH function

${{DVH}_{ij}(D)} = {1 - {\sum\limits_{\overset{\sim}{D}}^{D}\;{{\left\lbrack \frac{V_{ij}^{\prime}\left( \overset{\sim}{D} \right)}{V\left( {SS}_{ij} \right)} \right\rbrack \cdot \Delta}\; D}}}$was used for comparison between clinical DVHs and the predicted DVHs.

The boundary distance vector is given by Equation 1 below.{right arrow over (r _(l))}({right arrow over (x)})=min{{right arrowover (x)}−{right arrow over (X)}}∀{right arrow over (X)}∈SS _(ij)  (1)

In Equation 1, {right arrow over (r_(l))}({right arrow over (x)})expresses the smallest magnitude vector that would translate a positionvector {right arrow over (x)} (in any coordinate system) to the boundarysurface of the PTV (i.e., a position on the PTV boundary). While somefeatures of IMRT dose distributions may in fact be correlated to theorientation components of the boundary distance vector, this experimentconsiders the magnitude as a spatial correlate, embodied in the boundarydistance shown in Equation 2 below.r _(i)({right arrow over (x)})−∥{right arrow over (r _(l))}({right arrowover (x)})∥  (2)

Equation 2 expresses the minimum distance between any point and the PTVsurface boundary. Computing the boundary distance for a given instanceis a purely geometric operation. FIG. 3A illustrates a vector fieldrepresentation of {right arrow over (r_(l))}({right arrow over (x)})around PTV contour SS_(i1) (solid black) and FIG. 3B is an isodistancecontour map representation of the scalar field r_(i)({right arrow over(x)}). The connection between the boundary distance and an IMRT dosedistribution is as yet undetermined, but the familiar notion of doseconformality is equivalent to a negative correlation betweenD_(i)({right arrow over (x)}) and r_(i)({right arrow over (x)}), atleast at small boundary distances.

The structure sets SS_(ij) can be recast as the locus of points thatidentify each anatomical construct. Should this data be expressed interms of contours (sequence of closed loops) or masks (matrix of voxelswith binary representation of occupied positions), SS_(ij) identifiesany position {right arrow over (x)} as either inside or outside thej^(th) structure of the i^(th) dataset. This interpretation of SS_(ij)combined with the definition of r_(i)({right arrow over (x)}) yield thenew object A_(ijk), which is defined in Equation 3 below.A _(ijk) ≡r _(k) ∩SS _(ij)  (3)

In Equation 3, (k−1)δ<r_(k)≤kδ with k=1 . . . ∞ and δ being a finitedistance interval. Any overlap of the j^(th) structure with the PTV isencompassed In A_(ijk) ≡ SS_(i1) ∩SS_(ij). Thus, A_(ijk) represents thelocus of points inside the j^(th) structure of the i^(th) dataset thatreside between a specified interval of distance from the PTV boundary,as shown in FIG. 4. More specifically, FIG. 4 is a diagrammaticrepresentation of geometric constructs r_(i)({right arrow over (x)}) andA_(ijk).

A_(ijk) is itself a structure and satisfies the geometric relationshipSS_(ij)=A_(ij0) ∪A_(ij1) ∪A_(ij2) . . . ∪A_(ij∞). Operations on D_(i)and A_(ijk) yield X_(ijk), the differential DVH of A_(ijk). X_(ijk) canbe considered a “sub-DVH” of the total organ DVH (as shown in FIGS. 5Aand 5B), and as shown in Equation 4 below,V′ _(ij)−Σ_(k=0) ^(∞) X _(ijk) ·V(A _(ijk))  (4)where V(A_(ijk)) is the volume of A_(ijk). FIG. 5A is a graphicaldepiction of the j^(th) OAR's differential DVH V′_(ij) as summation overthe X_(ijk) sub-DVHs. FIG. 5B is more familiar cumulative DVH view of

${{DVH}_{ij}(D)} = {1 - {\sum\limits_{\overset{\sim}{D}}^{D}\;{{\left\lbrack \frac{V_{ij}^{\prime}\left( \overset{\sim}{D} \right)}{V\left( {SS}_{ij} \right)} \right\rbrack \cdot \Delta}\; D}}}$for an OAR.

The X_(ijk) sub-DVHs depicted in FIG. 5A are idealized distributions.Real clinical distributions will exhibit more variability within adistribution. In FIGS. 6A-6D, rectum sub-volume DVHs X_(ijk) for aclinical prostate case are shown for (a) k=O, (b) k=1, (c) k=4, and (d)k=10 at δ=3 mm. The solid curve is a fit to each of the observedsub-DVHs with the skew-normal distribution and its three fittingparameters p₁, p₂, and p₃:

$\begin{matrix}{{f\left( {p_{1},p_{2},{p_{3};D}} \right)} = {\frac{1}{\pi\; p_{2}}e^{\frac{{({D - p_{1}})}^{2}}{2\; p_{2}^{2}}}{\int_{- \infty}^{\frac{p_{3}{({D - p_{1}})}}{p_{2}}}{e^{- \frac{t^{2}}{2}}{dt}}}}} & (5)\end{matrix}$

Equation 5 employs three fitting parameters: p 1 (location), p 2(scale), and p₃ (shape). One practical limitation of using theskew-normal distribution as the basis function for a differential DVH isthat Equation 5 is normalized on the interval from −∞ to +∞, while a DVHis only defined from 0 to +∞. This is readily alleviated by arenormalized skew-normal distribution, Φ(p₁, p₂, p₃; D), given byEquation 6 below.

$\begin{matrix}{{\Phi\left( {p_{1},p_{2},{p_{3};D}} \right)} = \frac{f\left( {p_{1},p_{2},{p_{3};D}} \right)}{\sum\limits_{D = 0}^{\infty}\;{f\left( {p_{1},p_{2},{p_{3};\overset{\sim}{D}}} \right)}}} & (6)\end{matrix}$

Whether a single fitting function with a finite set of parameters iscapable of modeling X_(ijk) for all k will be determined by concordanceto the observed training sets. The renormalized skew-normal distributionis but one possible universal fitting function that may be described bya general function Φ(p₁, p₂ . . . p_(Q); D) with q=1 . . . Q parametersp_(Q). As each OAR for each patient will be fit with this function, thefitting function for each individual X_(ijk) will be given by Equation7, below.X _(ijk,fit)(D)=Φ[p _(ijk1) ,p _(ijk2) . . . p _(ijkQ) ;D]  (7)

After each sub-DVH fit is obtained, e.g. via least-squares minimization,the totality of the training sets' geometric and dosimetricrelationships is accessible through analysis of the fitting parametersp_(ijkq). Averaging over all training sets gives the mean fittingparameter as shown in Equation 8, as well as any other statisticalanalyses afforded by the sample size, e.g. standard deviation.

$\begin{matrix}{{\overset{\_}{p}}_{jkq} - {\frac{1}{N}{\sum\limits_{i = 1}^{N}\; p_{ijkq}}}} & (8)\end{matrix}$Further, as p_(ijkq) is a direct function of increasing boundarydistance through r_(k) any functional fit (e.g. generalized polynomial)through p _(jkq) yields a deterministic trajectory p_(jq)(k) of theq^(th) parameter in the j^(th) OAR. The p_(jq)(k) trajectories in turnyield the resultant predicted DVH for the j^(th) structure in the i^(th)dataset, as shown in Equation 9,V′ _(ij,pred)=Σ_(k=0) ^(∞)Φ[p _(j1)(k),p _(j2)(k), . . . p_(jQ)(k);D]·V(A _(ijk)).  (9)

Goodness-of-fit analyses comparing V′_(ij,pred) to the measured V′_(ij)can inform the quality of the ensemble averaging fits in individualcases, as well as identify outliers with respect to the mean, asdiscussed in more detail below. It is important to stress that theelements of Equation 9 are entirely geometric, while the outputdistribution is the full does volume histogram of the j^(th) OAR for anypatient. As the function Φ[p_(j1)(k), p_(j2)(k), . . . p_(jQ)(k); D]represents the mathematical summary of prior experience, this relationand the formalism that led to it illustrates an exemplary embodiment ofthis disclosure.

In the case of “new” patients, i.e. The introduction of a new datasetfor which there is no measured dose matrix D_(N+1), geometric operationsalone on SS_((N+1)j) yield A_((N+1)jk) and V(A_((N+1)jk)), which in turnmay be employed in Equation 9 to obtain a predicted DVH for anystructure with an associated function Φ[p_(j1)(k), p_(j2)(k), . . .p_(jQ)(k); D]. A predicted DVH, informed by the N prior cases, is thusavailable for any new dataset even in the absence of any dosimetricinformation as long as the clinical goals are identical to the trainingsets.

To validate this formalism, clinically-approved treatment plans forintact prostate IMRT and head & neck IMRT were utilized as training datato develop models that generate predictive DVHs for rectum, bladder, andparotid glands. A general framework outlined in this section wasrepeated for each OAR. Obtaining predictive DVHs for a given OAR isachieved by six distinct steps which include: 1) data acquisition, 2)dose-to-distance modeling, 3) fitting of parameter trajectories, 4)model validation, 5) outlier identification, and 6) model refinement.

N site-similar patients were randomly identified from our clinicaldatabase. Each site-similar IMRT treatment plan was clinically approvedaccording to the same institutional planning goals (shown in Table 1),and consisted of a structure set (SS_(ij)) and a dose matrix (D_(i))with 3 mm×3 mm×3 mm voxel size that was developed with a commercialtreatment planning system (Pinnacle³, a product of Philips MedicalSystems of Andover, Mass.).

IMRT delivery on conventional linear accelerators is typicallyaccomplished using co-planar beam arrangements. Co-planar deliveryviolates the isotropic assumptions inherent to the scalar boundarydistance formalism because the negative dose gradient underneathcollimating jaws is intrinsically greater than the in-field dosegradient achieved via intensity modulation. To restore the centralassumptions of this work, the in-field portion of the OAR was consideredseparately from the out-of-field portion of the OAR, as shown in FIG. 7.Alternate embodiments may instead focus on the orientation components ofthe boundary distance vectors, an approach that may obviate the need forthe in-field and out-of-field designations.

More specifically, FIGS. 8A-8C illustrate a distribution of in-fieldrectum parameters for all training sets. FIGS. 8D-8F illustrate afitting p _(jkq)±SD_(jkq) with generalized polynomial function. Each OARmodel thus contains two models, in-field and out-of-field, that aresummed to give the final predictive DVH, as shown in Equation 10 below.

$\begin{matrix}{V_{{ij},{pred}}^{\prime} = {\sum\limits_{k = 0}^{\infty}\;\left\lbrack {{{\Phi\left\lbrack {{p_{j\; 1}^{IN}(k)},{p_{j\; 2}^{IN}(k)},{{\ldots\mspace{14mu}{p_{jQ}^{IN}(k)}};D}} \right\rbrack} \cdot {V\left( A_{ijk}^{IN} \right)}} + {{\Phi\left\lbrack {{p_{j\; 1}^{OUT}(k)},{p_{j\; 2}^{OUT}(k)},{{\ldots\mspace{14mu}{p_{jQ}^{OUT}(k)}};D}} \right\rbrack} \cdot {V\left( A_{ijk}^{OUT} \right)}}} \right\rbrack}} & (10)\end{matrix}$

The renormalized skew normal distribution given by equation 5 wasemployed as a candidate fitting function for all sites, training sets,and OARs explored. This probability distribution function was used todetermine three parameters, location (p₁), scale (p₂), and shape (p₃),via least-squares minimization for all X_(ijk).

A mean fitting parameter p _(jkq) for each PTV shell is obtained byaveraging each parameter p_(jkq) over all training sets for both thein-field and out-of-field OAR. Statistical noise for the sample isassessed through determining the standard deviation of the data used tocalculate all mean fitting parameters, as shown in Equation 11 below.

$\begin{matrix}{{SD}_{jkq} = \sqrt{\frac{1}{N - 1}\left( {p_{ijkq} - {\overset{\_}{p}}_{jkq}} \right)^{2}}} & (11)\end{matrix}$shown as error bars in FIGS. 8C-8F.

Plotting the mean fitting parameter for location (p₁) as a function ofdistance for both the in-field and out-of-field OAR provides insightinto the manner by which the dose in each shell changes as a function ofkδ. Similarly, plotting the mean fitting parameter for scale (p₂) as afunction of kδ for both the in-field and out-of-field OAR providesinsight into the spread or variation of dose values in each shell.Finally, plotting the mean fitting parameter for shape as a function ofkδ provides insight into how the shape of the sub-DVH changes as afunction of distance (i.e. is the tail of the distribution pointedtoward low-dose or high-dose). The shape parameter (p₃) was only allowedto vary between [−10,10] since values outside of this range result inminimal effect on the shape of the distribution.

A generalized polynomial of order B was employed to fit the evolution ofthe p _(jkq) parameters, as shown in Equation 12 below,p _(jq)(k)=Σ_(b=1) ^(B)α_(jqb)·(kδ)²  (12)where the maximal order B was chosen on a case-by-case basis and thecoefficients α_(jqb) were determined through least-squares minimization.Each p _(jkq) for a given k is weighted by

$w_{jkq} = {\frac{1}{{SD}_{ijq}}.}$The function p_(jq)(k) accounts for any mean fitting parameters at agiven k that may be statistical outliers. FIGS. 8D-8F display examplesof the p_(jq)(k) fits set against p _(jkq) (open circles) and SD_(jkq)(error bars) for the in-field rectum cohort.

In order to assess the efficacy of the developed model on new patientdata, predictive DVHs were obtained for an independent set of validationpatients that were not part of the training data cohort. The accuracy ofthe model was assessed by comparing each predicted cumulative DVH,DVH_(ij,pred)(D), to the clinically-approved plan's cumulative DVH,DVH_(ij)(D). Comparing cumulative DVHs is preferred at this stagebecause of their connection to established clinical endpoints. WereDVH_(ij,pred)(D) a fit to DVH_(ij)(D) standard goodness-of-fit analysessuch as chi-squared tests would be appropriate. However, as the employedcurve-fitting methods described leave no degrees of freedom at thisstage, it becomes more difficult to quantify the discrepancy between thepredicted DVH and the clinical DVH in a meaningful way. A singular valuethat measures this discrepancy can be found in the sum of residuals, asshown in Equation 13 belowSR _(ij)=Σ_(D=0) ^(∞)ε_(ij)(D)  (13)whereε_(ij)(D)−[DVH _(ij)(D)−DVH _(ij,pred)(D)]·ΔD  (14)with the dose bin size included in the product to eliminate bin sizedependence. More traditional error analyses employ sums of squaredresiduals, but this is not appropriate here as negative residuals(clinical plan bettering the prediction at a given dose) are not onequal footing with positive residuals (prediction bettering clinicalplan at a given dose).

As a major goal of the predictive DVH methodology is the identificationof sub-optimal plans, it is important to separate the outlieridentification task from any goodness-of-fit analysis used for modelvalidation. As the sum residuals makes no distinction between positiveε(D) values (predicted DVH betters the clinical DVH), and negative ε(D)values (clinical DVH betters the predicted DVH), the identification ofsub-optimal plans was accomplished by use of a restricted sum ofresiduals, as shown in Equation 15 below,RSR _(ij)=Σ_(D=0) ^(∞)ε_(ij) ⁺(D)  (15)where

$\begin{matrix}{{ɛ^{+}(D)} = \left\{ {\begin{matrix}{{ɛ(D)},} & {{{if}\mspace{14mu}{ɛ(D)}} > 0} \\{0,} & {{{if}\mspace{14mu}{ɛ(D)}} \leq 0}\end{matrix}.} \right.} & (16)\end{matrix}$

A schematic of both the goodness-of-fit analysis and the outlieridentification analysis can be seen in FIGS. 9A-9C. Large values ofRSR_(ij) signal a patient for which the clinical DVH exceeds thepredicted DVH by a considerable amount compared to other site-similartreatment plans, and thus serves as a surrogate for the identificationof clinical DVHs that appear to have sub-optimal OAR sparing.

The planning process for these patients was repeated (“re-planning”) toestablish the true limit of OAR sparing. During re-planning, care wastaken to hold constant or improve PTV dosimetric aspects and maintainall other OAR DVH sparing within the dosimetric objective list inTable 1. A refined model was obtained by repeating the modeling processas described above on the training data sets that remain after excludingthe correctly identified sub-optimal plans. This refined model was againevaluated on the same set of independent validation patients. Analysisof the sum of squared residuals was completed both before and aftermodel refinement.

FIGS. 10A and 10B illustrate two-stage validation of predictive DVHmodeling. FIG. 10A shows an AVERAGE model that is trained with Nclinical patient plans. The accuracy of the AVERAGE model is analyzedboth by an analysis of its performance on the training data as well asits ability to correctly predict the DVHs of an equivalent sample of Mpatients in a sequestered validation set. Equivalent performance betweentraining and validation sets confirms the ability of modeling process tosubstantially accurately predict DVHs. FIG. 10B shows use of the AVERAGEmodel on the training data sample, outliers with relatively high RSR(Equation 15) are identified as potentially sub-optimal plans. Themodeling process is repeated without inclusion of these outliers,yielding the REFINED model. The predicted DVH gains per patient arerepresented by the RSR values obtained in application of the REFINEDmodel to the entire training sample. Verifying the predicted gains wasaccomplished by careful re-planning of each of the training patients inan attempt to increase organ sparing. Quantitative comparison betweenthe re-plan DVHs and the original DVHs was accomplished by computing thesuch of residuals between them, removing the predicted DVH resultsentirely from this quantity.

Since each OAR has a finite size and a finite number of patients wereused to develop each model, our statistics decrease for points at largedistances from the PTV. Therefore, at a determined distance from the PTVwhere the OAR statistics become sparse, the mean parameter trajectoryfits were held at a constant value. These constants varied for eachorgan depending on the number of patients with non-zero volume of OAR ineach PTV ring.

Twenty intact prostate patients treated with IMRT were used to obtainpredictive DVH models for the rectum and bladder, denoted as the initialAVERAGE model. For both bladder and rectum respectively, five patientsout of the initial twenty patient cohort were identified as outliers andremoved from the training set to develop the REFINED model. FIGS.12A-12F demonstrates both AVERAGE and REFINED models' DVH predictionsagainst three clinically-approved plans for both bladder and rectum.Both demonstrate good concordance, but the REFINED model more closelymatches the observed DVHs.

FIGS. 14A-14F show the identification of sub-optimal plans in thetraining cohort by the AVERAGE model and the demonstration throughre-planning of the realized improvements.

FIGS. 15A-15F are graphs demonstrating the concordance of the twopredictive DVH models to the clinically-approved rectum and bladder DVHsfrom the validation set, i.e. “new” plans unseen by the model.

FIGS. 13A and 13B show the strong correlation between predicted gains(RSR, Equation 15) and actualized gains (SR_(orig)−SR_(replan), Equation13) for the bladder and rectum, respectively. These data alsodemonstrate the low rate of false positives (minimal population in thelower right portion of the graph) and false negatives (minimalpopulation in the upper left portion of the graph).

Repeating this process for the parotid gland OAR in head-and-neck IMRT,24 clinically-approved treatment plans were used as a training cohort todevelop an AVERAGE model. FIGS. 16A-16F show the parameter trajectoriesfor the in-field and out-of-field portions of the parotid model.

Because of the small initial sample size, the model validation step wasomitted and only the second validation procedure (FIG. 10B) wasconducted. Five patients were identified as potentially sub-optimal andremoved from the training cohort to develop the REFINED model. FIGS.17A-12F demonstrates both AVERAGE and REFINED models' DVH predictionsagainst six clinically-approved plans for the parotid. Both demonstratedgood concordance with the REFINED model more closely matching theobserved DVHs.

FIGS. 18A-18C show the identification of sub-optimal plans in thetraining cohort by the AVERAGE model and the demonstration throughre-planning of the realized improvements.

FIG. 19 shows the strong correlation between predicted gains (RSR,Equation 15) and actualized gains (SR_(orig)−SR_(replan). Equation 13).These data also demonstrate the low rate of false positives (minimalpopulation in the lower right portion of the graph) and false negatives(minimal population in the upper left portion of the graph).

The SR and RSR formalism for comparing DVHs is but one method ofcomparison most appropriate for parallel-functioning organs such as theparotids or the liver. It is known that in serial organs like the rectumor the spinal cord the high dose portion of the DVH is most correlatedto radiation-induced complications. It is possible to consider insteadspecific DVH point differences. e.g., ε (40 Gy) or ε (65 Gy), thoughthis would ignore all other parts of the DVH curves. One modification ofthe DVH comparison could immediately convert into an existingradiobiological formalism via the generalized restricted sum ofresiduals (gRSR), as shown in Equation 17 belowgRSR _(ij)=Σ_(D=0) ^(∞)ε_(ij) ⁺(D)·D ^(α−1)  (17)where α is the order parameter in the introduction of generalizedequivalent uniform dose (gEUD). In a one-to-one correspondence to thegEUD concept, α=1 for parallel organs and gRSR reverts to the simplerestricted sum of residuals. For serial OARs, the value of α will begreater than unity, meaning the higher dose deviations will receivehigher weighting as compared to the lower dose differences. Currentunderstanding of organ response can be immediately brought to bear whendeveloping predictive dose-volume models for specific organs.

The embodiments illustrated and described herein as well as embodimentsnot specifically described herein but within the scope of aspects of theinvention constitute exemplary means for correlating a dose-volumerelationship (e.g., mean dose, dose-volume histogram, equivalent uniformdose, 3-D dose distribution) to boundary distance vectors from thevoxels of one or more OAR to a boundary of a PTV.

The order of execution or performance of the operations in embodimentsof the invention illustrated and described herein is not essential,unless otherwise specified. That is, the operations may be performed inany order, unless otherwise specified, and embodiments of the inventionmay include additional or fewer operations than those disclosed herein.For example, it is contemplated that executing or performing aparticular operation before, contemporaneously with, or after anotheroperation is within the scope of aspects of the invention.

When introducing elements of aspects of the invention of the embodimentsthereof, the articles “a,” “an,” “the,” and “said” are intended to meanthat there are one or more of the elements. The terms “comprising,”“including,” and “having” are intended to be inclusive and mean thatthere may be additional elements other than the listed elements.

Having described aspects of the invention in detail, it will be apparentthat modifications and variations are possible without departing fromthe scope of aspects of the invention as defined in the appended claims.As various changes could be made in the above constructions, products,and methods without departing from the scope of aspects of theinvention, it is intended that all matter contained in the abovedescription and shown in the accompanying drawings shall be interpretedas illustrative and not in a limiting sense.

What is claimed is:
 1. A system for developing a predictive dose-volumerelationship for a radiation therapy treatment, the system comprising: amemory area storing a training set of training treatment plans, eachtraining treatment plan including a three-dimensional representation ofone or more planning target volumes and one or more organs-at-risk of aprior patient, and an amount of radiation delivered to one or moreplanning target volumes and the one or more organs-at-risk; and aprocessor that executes instructions that cause the system to: access,from the memory area, the training set of treatment plans; determine,for each training treatment plan, a plurality of minimum distancevectors between discrete volume elements of the one or moreorgans-at-risk and a boundary surface of one or more planning targetvolumes; determine, for each training treatment plan, a set ofdose-volume relationships corresponding to irradiation of at least oneplanning target volume and at least one organ-at-risk; develop a modelthat predicts dose-volume relationships for a new patient usingthree-dimensional representations of a planning target volume of the newpatient and one or more organs-at-risk of the new patient, the modelbeing derived from correlations between the dose-volume relationshipsand minimum distance vectors; predict dose-volume relationships for theplanning target volume and the one or more organs-at-risk of the newpatient using the model; output predicted dose-volume relationships forthe planning target volume and the one or more organs-at-risk of the newpatient to a radiation therapy treatment device; and treat the newpatient based at least in part on the predicted dose-volumerelationships for the planning target volume and the one or moreorgans-at-risk of the new patient.
 2. The system of claim 1, wherein theprocessor is programmed to optimize the model that predicts dose-volumerelationships, by: applying the developed model to each trainingtreatment plan in the training set to produce a predicted dose volumerelationship for each training treatment plan; comparing the predicteddose-volume relationship of each training treatment plan to itsdetermined dose-volume relationship; and revising the model thatpredicts dose-volume relationships for a new patient based on thecomparing of the predicted dose-volume relationship of each trainingtreatment plan to its determined dose-volume relationship.
 3. The systemof claim 2, wherein the processor is further programmed to optimize themodel that predicts dose-volume relationships, by identifying suboptimaltraining treatment plans for which the determined dose-volumerelationships indicate greater radiation received by the at least oneorgan-at-risk than the predicted dose-volume relationships.
 4. Thesystem of claim 3, wherein revising the model that predicts dose-volumerelationships comprises deriving the model from correlations between thedetermined dose-volume relationships and minimum distance vectorswithout including the determined dose-volume relationships and minimumdistance vectors from the suboptimal training treatment plans.
 5. Thesystem of claim 3, wherein identifying suboptimal training treatmentplans comprises determining a restricted sum of residuals of thepredicted dose-volume relationship for each training treatment plan andits determined dose-volume relationship.
 6. The system of claim 1,wherein the processor is programmed to develop the model that predictsdose-volume relationships by fitting an evolution of skew-normalparameters as a function of the plurality of minimum distance vectors.7. The system of claim 1, wherein the processor is further programmedto: identify, for each training treatment plan, a plurality ofsub-volumes of the one or more organs-at-risk; and determine theplurality of minimum distance vectors between discrete volume elementsof the one or more organs-at-risk and a boundary surface of the planningtarget volume by determining a minimum distance vector between eachsub-volume of the one or more organs-at-risk and the one or moreplanning target volumes.
 8. The system of claim 7, wherein the processoris further programmed to determine a radiation dose received by eachsub-volume of the one or more organs-at-risk.
 9. The system of claim 1,wherein the processor is programmed to develop the model to require onlythe three-dimensional representation of the planning target volume ofthe new patient and one or more organs-at-risk of the new patient topredict dose-volume relationships for the new patient.
 10. A radiationtherapy system for predicting a dose-volume relationship for a radiationtherapy treatment, the system comprising: a memory device storing: amodel that predicts dose-volume relationships for a radiation therapytreatment using three-dimensional representations of a planning targetvolume of a new patient and one or more organs-at-risk of the newpatient, the model being derived from correlations between thedose-volume relationships and minimum distance vectors of a plurality ofpatients; and new patient data including three-dimensionalrepresentations of a planning target volume of a new patient and one ormore organs-at-risk of the new patient; a display device; and aprocessor that executes instructions to cause the radiation therapysystem to: access the new patient data; calculate a plurality of minimumdistance vectors between discrete volume elements of the one or moreorgans-at-risk of the new patient and a boundary surface of the planningtarget volume of the new patient; predict dose-volume relationships forthe planning target volume and the one or more organs-at-risk of the newpatient using the stored model and the calculated minimum distancevectors for the new patient; display the predicted dose-volumerelationships for the planning target volume and the one or moreorgans-at-risk of the new patient on the display device; output thepredicted dose-volume relationships for the planning target volume andthe one or more organs-at-risk of the new patient to a radiation therapytreatment device; and treat the new patient based at least in part onthe predicted dose-volume relationships for the planning target volumeand the one or more organs-at-risk of the new patient.
 11. The radiationtherapy system of claim 10, wherein processor is programmed to treat thenew patient using a linear accelerator.
 12. The radiation therapy systemof claim 10, wherein the processor is further programmed to: receive thethree-dimensional representations of the planning target volume of thenew patient and the one or more organs-at-risk of the new patient; andstore the received three-dimensional representations of the planningtarget volume of the new patient and the one or more organs-at-risk ofthe new patient in the memory device.
 13. The radiation therapy systemof claim 12, wherein the processor is programmed to receive thethree-dimensional representations of the planning target volume of thenew patient and the one or more organs-at-risk of the new patient from adiagnostic imaging source.
 14. A method comprising: receiving a trainingset of training treatment plans, each training treatment plan includingradiation therapy treatment including a three-dimensional representationof a planning target volume and one or more organs-at-risk of a priorpatient, and an amount of radiation delivered to the planning targetvolume and the one or more organs-at-risk of the prior patient;determining, for each training treatment plan, a plurality of minimumdistance vectors between discrete volume elements of the one or moreorgans-at-risk and a boundary surface of the planning target volume;determining, for each training treatment plan, a dose-volumerelationship corresponding to an irradiation of at least oneorgan-at-risk; developing a model that predicts dose-volumerelationships for a new patient using three-dimensional representationsof a planning target volume of the new patient and one or moreorgans-at-risk of the new patient, the model being derived fromcorrelations between the determined dose-volume relationships andminimum distance vectors; predicting dose-volume relationships for theplanning target volume and the one or more organs-at-risk of the newpatient using the model; outputting predicted dose-volume relationshipsfor the planning target volume and the one or more organs-at-risk of thenew patient to a radiation therapy treatment device; and treating thenew patient based at least in part on the predicted dose-volumerelationships for the planning target volume and the one or moreorgans-at-risk of the new patient.
 15. The method of claim 14, furthercomprising: applying the developed model to each training treatment planin the training set to produce a predicted dose volume relationship foreach training treatment plan; comparing the predicted dose-volumerelationship of each training treatment plan to its determineddose-volume relationship; and revising the model that predictsdose-volume relationships for a new patient based on the comparing ofthe predicted dose-volume relationship of each training treatment planto its determined dose-volume relationship by identifying suboptimaltraining treatment plans for which the determined dose-volumerelationships indicate greater radiation received by the at least oneorgan-at-risk than the predicted dose-volume relationships.
 16. Themethod of claim 15, wherein revising the model that predicts dose-volumerelationships comprises deriving the model from correlations between thedetermined dose-volume relationships and minimum distance vectorswithout including the determined dose-volume relationships and minimumdistance vectors from the suboptimal training treatment plans.
 17. Themethod of claim 15, further comprising identifying, for each trainingtreatment plan, a plurality of sub-volumes of the one or moreorgans-at-risk, and wherein determining the plurality of minimumdistance vectors between discrete volume elements of the one or moreorgans-at-risk and a boundary surface of the planning target volumecomprises determining a minimum distance vector between each sub-volumeof the one or more organs-at-risk and the planning treatment volume. 18.The method of claim 17, further comprising determining a radiation dosereceived by each sub-volume of the one or more organs-at-risk.